13,346 research outputs found

    Spectral networks and Fenchel-Nielsen coordinates

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    We explain that spectral networks are a unifying framework that incorporates both shear (Fock-Goncharov) and length-twist (Fenchel-Nielsen) coordinate systems on moduli spaces of flat SL(2,C) connections, in the following sense. Given a spectral network W on a punctured Riemann surface C, we explain the process of "abelianization" which relates flat SL(2)-connections (with an additional structure called "W-framing") to flat C*-connections on a covering. For any W, abelianization gives a construction of a local Darboux coordinate system on the moduli space of W-framed flat connections. There are two special types of spectral network, combinatorially dual to ideal triangulations and pants decompositions; these two types of network lead to Fock-Goncharov and Fenchel-Nielsen coordinates respectively.Comment: 63 pages; v2: expository improvements, journal versio

    Exploring Two Novel Features for EEG-based Brain-Computer Interfaces: Multifractal Cumulants and Predictive Complexity

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    In this paper, we introduce two new features for the design of electroencephalography (EEG) based Brain-Computer Interfaces (BCI): one feature based on multifractal cumulants, and one feature based on the predictive complexity of the EEG time series. The multifractal cumulants feature measures the signal regularity, while the predictive complexity measures the difficulty to predict the future of the signal based on its past, hence a degree of how complex it is. We have conducted an evaluation of the performance of these two novel features on EEG data corresponding to motor-imagery. We also compared them to the most successful features used in the BCI field, namely the Band-Power features. We evaluated these three kinds of features and their combinations on EEG signals from 13 subjects. Results obtained show that our novel features can lead to BCI designs with improved classification performance, notably when using and combining the three kinds of feature (band-power, multifractal cumulants, predictive complexity) together.Comment: Updated with more subjects. Separated out the band-power comparisons in a companion article after reviewer feedback. Source code and companion article are available at http://nicolas.brodu.numerimoire.net/en/recherche/publication

    Practical solutions for a dock assignment problem with trailer transportation.

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    We study a distribution warehouse in which trailers need to be assigned to docks for loading or unloading. A parking lot is used as a buffer zone and transportation between the parking lot and the docks is performed by auxiliary resources called terminal tractors. Each incoming trailer has a known arrival time and each outgoing trailer a desired departure time. The primary objective is to produce a docking schedule such that the weighted sum of the number of late outgoing trailers and the tardiness of these trailers is minimized; the secondary objective is to minimize the weighted completion time of all trailers, both incoming and outgoing. The purpose of this paper is to produce high-quality solutions to large instances that are comparable to a real-life case. We implement several heuristic algorithms: truncated branch and bound, beam search and tabu search. Lagrangian relaxation is embedded in the algorithms for constructing an initial solution and for computing lower bounds. The different solution frameworks are compared via extensive computational experiments.Dock assignment; Multicriteria scheduling; Branch and bound; Beam search; Lagrangian relaxation; Tabu search;

    On the nature of the lexicon: the status of rich lexical meanings

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    The main goal of this paper is to show that there are many phenomena that pertain to the construction of truth-conditional compounds that follow characteristic patterns, and whose explanation requires appealing to knowledge structures organized in specific ways. We review a number of phenomena, ranging from non-homogenous modification and privative modification to polysemy and co-predication that indicate that knowledge structures do play a role in obtaining truth-conditions. After that, we show that several extant accounts that invoke rich lexical meanings to explain such phenomena face problems related to inflexibility and lack of predictive power. We review different ways in which one might react to such problems as regards lexical meanings: go richer, go moderately richer, go thinner, and go moderately thinner. On the face of it, it looks like moderate positions are unstable, given the apparent lack of a clear cutoff point between the semantic and the conceptual, but also that a very thin view and a very rich view may turn out to be indistinguishable in the long run. As far as we can see, the most pressing open questions concern this last issue: can there be a principled semantic/world knowledge distinction? Where could it be drawn: at some upper level (e.g. enriched qualia structures) or at some basic level (e.g. constraints)? How do parsimony considerations affect these two different approaches? A thin meanings approach postulates intermediate representations whose role is not clear in the interpretive process, while a rich meanings approach to lexical meaning seems to duplicate representations: the same representations that are stored in the lexicon would form part of conceptual representations. Both types of parsimony problems would be solved by assuming a direct relation between word forms and (parts of) conceptual or world knowledge, leading to a view that has been attributed to Chomsky (e.g. by Katz 1980) in which there is just syntax and encyclopedic knowledge
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